Narat Charupat

Optimal asset allocation in life annuities: a note

Abstract In this note, we derive the optimal utility-maximizing asset allocation between a risky and risk-free asset within a variable annuity (VA) contract, which is a US-based savings and decumulation investment product. We are interested in the interaction between financial risk, mortality risk and consumption, towards the end of the life cycle. Our main result is that for constant relative risk aversion (CRRA) preferences and geometric Brownian motion (GBM) dynamics, the optimal asset allocation during the annuity decumulation (payout) phase is identical to the accumulation (savings) phase, which is the classical Merton [J. Econ. Theory 3 (1971) 373] solution.

Margin, Short Selling, and Lotteries in Experimental Asset Markets

The robustness of bubbles and crashes in markets for assets with finite lives is perplexing. This paper reports the results of experimental asset markets in which participants trade two assets. In some markets, price bubbles form. In these markets, traders pay higher prices for the asset with lottery characteristics (i.e., a claim on a large, unlikely payoff). However, institutional design has a significant impact on deviations in prices from fundamental values, particularly for an asset with lottery characteristics. Price run-ups and crashes are moderated when traders finance purchases of the assets themselves and are allowed to short sell.

Bubbles in Experimental Asset Markets: Irrational Exuberance No More

The robustness of bubbles and crashes in markets for finitely lived assets is perplexing. This paper reports the results of experimental asset markets in which participants trade two assets. In some markets, price bubbles form. In these markets, traders will pay even higher prices for the asset with lottery characteristics, i.e., a claim on a large, unlikely payoff. However, institutional design has a significant impact on deviations in prices from fundamental values, particularly for an asset with lottery characteristics. Price run-ups and crashes are moderated when traders finance purchases of the assets themselves and are allowed to short sell.

Recent developments in exchange-traded fund literature: Pricing efficiency, tracking ability, and effects on underlying securities

Purpose - The purpose of this paper is to provide a brief review of three strands of the literature on exchange-traded funds. Design/methodology/approach - The paper starts with a review of the history of the growth of exchange-traded funds and their characteristics. The paper then examines the key factors and findings of the existing studies on, respectively, the pricing efficiency, the tracking ability/performance, and the impact on underlying securities of exchange-traded funds. Findings - Although there has been a substantial amount of research conducted to advance our knowledge on the trading, management, and effect of exchange-traded funds, the findings are still far from conclusive in addressing a number of research questions. Practical implications - Investors and other market participants will find this review informative in enhancing the understanding of exchange-traded funds. Originality/value - By highlighting the general theme of the related research findings, the paper provides a systematic review of the existing literature that future researchers can utilize in developing their research agenda.

Probability Judgment Error and Speculation in Laboratory Asset Market Bubbles

In 12 sessions conducted in a typical bubble-generating experimental environment, we design a pair of assets that can detect both irrationality and speculative behavior. The specific form of irrationality we investigate is the probability judgment error associated with low-probability, high-payoff outcomes. Independently, we test for speculation by comparing prices of identically paying assets in multiperiod versus single-period markets. We establish that aggregate irrationality measured in one dimension (probability judgment error) is associated with aggregate irrationality measured in another (bubble formation).

The Origins of Bubbles in Laboratory Asset Markets

In twelve sessions conducted in a typical bubble-generating experimental environment, we design a pair of assets that can detect both irrationality and speculative behavior. The specific form of irrationality we investigate is probability judgment error associated with low-probability, high-payoff outcomes. Independently, we test for speculation by comparing prices of identically paying assets in multiperiod versus single-period markets. When these tests indicate the presence of probability judgment error and speculation, bubbles are more likely to occur. This finding suggests that both factors are important bubble drivers.

MORTALITY SWAPS AND TAx ARBITRAGE IN THE CANADIAN INSURANCE AND ANNUITY MARKETS

The authors analyze a tax arbitrage opportunity that results from engaging in two seemingly counterintuitive transactions in the Canadian insurance market. Specifically, if an individual acquires a fixed immediate life annuity and then uses the periodic annuity income to fund a term-to-life insurance policy, these two transactions, which the authors refer to as a “mortality swap,” will generate a payoff pattern that is risk-free. In other words, a mortality swap replicates a risk-free security, albeit one with a stochastic liquidation date. The authors show theoretically that the rate of return on a mortality swap is equal to the risk-free rate on a before-tax basis, but exceeds it on an after-tax basis. This is confirmed by the results of the empirical test, which uses observed annuity and insurance quotes that already reflected adverse-selection and transaction costs. The authors also observe that the older an individual is and/or the higher his/her marginal tax rate is, the more he/she stands to gain from this tax arbitrage. This advantageous investment opportunity exists because of the arguably lenient method that Canadian authorities use to tax annuity income. The authors provide two major reasons that this method leads to an arbitrage opportunity. The authors then compare this method to that under the U.S. tax rules and show that the U.S. method renders tax arbitrage very unlikely. The demand for life insurance and annuities is usually attributed to risk aversion, consumption smoothing, and the desire for household protection. The authors’ findings provide an arbitrage-based reason for their demand. As a natural by-product, the authors’ research contains policy implications for the optimal taxation of annuities and insurance policies. Narat Charupat is assistant professor of finance at the DeGroote School of Business, McMaster University. Moshe Arye Milevsky is associate professor of finance at the Schulich School of Business, York University, and the Director of the Individual Finance and Insurance Decisions (IFID) Centre in Toronto, Canada. Financial support from the Life Underwriters Association of Canada (Charupat), the York University Research Authority, and the SSHRC (Milevsky) is gratefully acknowledged. The authors would like to thank Glenn Daily, Clarence Kwan, and the two anonymous referees for their helpful suggestions, as well as Lowell Aronoff (CANNEX), John Hitchcock (SunLife), Jon Archer (RBC), and Zale Newman (PanFinancial) for providing data on insurance and annuity quotes. Any errors are the authors’ responsibility.

The Annuity Duration Puzzle

We test whether life-contingent annuity prices promptly and fully adjust to changes in interest rates; a standard assumption made implicitly or explicitly in a growing annuity literature. Using a unique database consisting of over 3 million U.S. annuity quotes, we find that prices do not move as one might expect. Rather, prices adjust gradually and over a period of several weeks and often months, in response to certain -- and not necessarily riskless -- interest rate changes. In particular, we find that changes to the 30-year U.S. mortgage rate provide a better fit and indication of where annuity payouts are headed, compared to the 10-year swap rate, for example. In addition, we find that the sensitivity to interest rate changes (a.k.a. annuity duration) is asymmetric. Annuity prices react more rapidly and with greater sensitivity to an increase in the relevant interest rate compared to a decrease. Overall our findings are inconsistent with a financial economic view of a life annuity as a risk-free bond-like instrument, plus mortality credits. We believe that we are the first to examine the dynamic microstructure of annuity prices and that our results have implications for a wide swath of existing literature. This includes portfolio choice at retirement, the optimal timing of annuitization, the moneys worth ratio, the inference of mortality expectations from insurance prices as well as the valuation of pension liabilities.

The Sluggish and Asymmetric Reaction of Life Annuity Prices to Changes in Interest Rates

Many assume that in the short run, annuity prices promptly and efficiently respond to changes in interest rates. Using a unique database of quotes, we show this is not the case. Prices are less sensitive to changes in rates than expected, and responses are asymmetric. Prices react more rapidly and with greater sensitivity to an increase than to a decrease in rates. The results are robust, but there is a small degree of heterogeneity in the responses of different insurance companies. When rates increase, larger firms are slightly quicker to improve prices. The opposite is true when rates decline. In sum, we show that the microstructure of annuity dynamics is more complicated than (simply) adding mortality credits to bond yields.

Performance and Tracking Errors

The performance of ETFs is measured by tracking error, commonly defined as the deviation of the returns on net asset values (NAVs) of ETFs from the corresponding returns on the underlying benchmark indices. The deviation tells us how effective and efficient is the fund management in tracking the performance of the benchmark index and delivering the promised return. Unlike price deviations (as discussed in chapter 5), which are typically expected to be within the arbitrage bounds given the creation/redemption process of ETFs, any deviations of the returns on NAV from those of their underlying benchmarks can accumulate over time and thus significantly affect the long-term performance of the ETFs.